In a large bowl, beat the buttery spread, sugar, applesauce, and lemon juice on medium speed until light and fluffy.
Add the gluten free flour blend and lemon zest, mix to combine. Add the poppy seeds and mix. (If the dough seems too wet, add a bit more flour. Texture can vary with different gluten free flour blends).
Divide the dough into two parts, and shape into discs. Wrap the discs with plastic wrap and refrigerate for 2 hours, or freeze for about 30 minutes.
Preheat oven to 350 degrees F. Line two cookie sheets with parchment paper.
Lightly flour a rolling pin and rolling surface with gluten free flour. Place the dough on the surface and roll to about a ¼ inch thickness. (If the dough is too cold and stiff, you may have to let it warm up just a little bit before rolling.
Using a round cookie cutter, (or a different shape - flowers would be pretty!) cut out cookies, and quickly transfer them to the cookie sheets.
Bake at 350 for 12-14 minutes.
Cool for a few minutes on the cookie sheets, then transfer to a wire rack to cool completely.
Make the glaze:
Sift the confectioner's sugar into a mixing bowl.
Add the lemon juice, or water, depending on if you want a lemony glaze, or just a sugary glaze, and whisk. If the glaze is too thick, add more liquid.
Drizzle glaze over cooled cookies.
Notes
You can use regular all-purpose flour or white spelt flour if you don't need these to be gluten free.Store leftover cookies in an airtight container. They should stay fresh for about 5 days.